Please help me. Shaping problems

Hello.
I've been working with Illustrator for quite a while now but it's one thing that i just never learned how to do.

Let me explain:

Say you want a black rectangle shape with a white square in top left corner.
This is how i would do it.

Draw a black rectangle and a white square in it. Simple as that. Though the problem lies when you want an object to be placed behind the black rectangle but in front of the white square. For example something that you should see the edges of but not the whole shape.

This problem can be solved by doin this instead:

Draw a black rectangle, add anchor points where you want the square to be and shift drag the top left corner point to where you want it. I hope u get the idea.

But now the real problem appears:
What if you want it to be a circle in the rectangle? Or a half circle shape in a bigger circle? Help me here! Is there some way to remove parts of another shape with the shape tool?

for example, to make the half circle, you could draw a circle, then a square, put the square on the circle, select both the images, then click the "subtract from shape area" icon in the pathfinder menu. for the placement of the images, i would just draw them all on different layers, and then move them into position...im not sure if i'm understanding everything, but i've tried

Thanks so much, that was exactly what i was looking for
The reason i didn't want to make the little circle (or whatever ) in a layer in front was because i am lazy and wanted to put an object in front of the circle and behind the rectangel without having to be exact enough to just putting it in the circle and drawing the other line by hand.

Hopefully you understood now and thanks again.